This page has a Chinese version as 科学技术关联。

Research Questions

Given a patent sector, knowing how other patent sectors and scientific fields support this particular sector, and vice versa, how other patent sectors and scientific fields are supported by this particular sector, can be helpful for decision making on how to develop or exploit this particular sector.

Similarly, given a scientific field, knowing how other scientific fields and patent sectors support this particular field, and vice versa, how other scientific fields and patent sectors are supported by this particular field, can also be helpful for decision making on how to develop and exploit this scientific field.

It is not only for individual researchers and developers that answers to those questions can be informative, but also to policy makers and administrators in science and technology of enterprises or of a nation.

So, do we have method of analysis to answer those questions?

Method of analysis

direct linkage

One of the analysis can be a simple statistical analysis of the sci-tech matrix [math]\displaystyle{ X=\left(x^{i}_{j}\right)_{\left(N+M\right)\times\left(N+M\right)} }[/math], where there are N science fields denoted as [math]\displaystyle{ i,j }[/math] specifically and [math]\displaystyle{ a,b }[/math] generally and abstractly, and M patent sectors denoted as [math]\displaystyle{ \mu,\nu }[/math]specifically and [math]\displaystyle{ \alpha, \beta }[/math] generally and abstractly. Here a specific element [math]\displaystyle{ x^{i}_{j} }[/math] means the number of citations from papers/patents in class j to those of class i, ie, j citing i, or we say, i goes into and thus support j.

It can also be denoted respectively as [math]\displaystyle{ \begin{bmatrix}x^{a}_{b} & x^{a}_{\alpha}\\ x^{\alpha}_{a} & x^{\alpha}_{\beta}\end{bmatrix} }[/math], or sometimes in a sub matrix form [math]\displaystyle{ \begin{bmatrix}S & ST\\ TS & T\end{bmatrix} }[/math].

A direct linkage is defined to be the following direct forword input-output coefficient matrix [math]\displaystyle{ F }[/math], where [math]\displaystyle{ F^{i}_{j}=\frac{x^{i}_{j}}{X^{j}} }[/math] and [math]\displaystyle{ X^{j}=\sum_{k}x^{j}_{k} }[/math]is the total number of citations recieved by papers/patents in sector j, or we say the output of sector j in terms of the input-output analysis in Economics. Thus, [math]\displaystyle{ F^{i}_{j} }[/math] means how much input from i is required to produce one unit of output from sector j.

Similarly, we can define a direct Backword input-output coefficient matrix [math]\displaystyle{ B }[/math], where [math]\displaystyle{ B^{i}_{j}=\frac{x^{i}_{j}}{X_{i}} }[/math] and [math]\displaystyle{ X_{i}=\sum_{k}x^{k}_{i} }[/math] is the total number of citations initiated from papers/patents in sector i, or we say the input of sector i in terms of the input-output analysis in Economics. Thus, [math]\displaystyle{ B^{i}_{j} }[/math] means how much output is distributed to sector j for each unit of input goes into sector i.

In fact, we can also define two other matrices [math]\displaystyle{ MF^{i}_{j}=\frac{x^{i}_{j}}{X^{i}} }[/math] and [math]\displaystyle{ MB^{i}_{j}=\frac{x^{i}_{j}}{X_{j}} }[/math]. However, it can be shown that each calculation that we can do on matrices [math]\displaystyle{ MF, MB }[/math], we can correspodingly do on matrices [math]\displaystyle{ F, B }[/math]. Do we can always perform our analysis on [math]\displaystyle{ F, B }[/math] and later convert the result to those of [math]\displaystyle{ MF, MB }[/math]. Some might prefer to work with [math]\displaystyle{ MF, MB }[/math] better since they are in the forms of probability transfer matrices. For example, [math]\displaystyle{ MF^{i}_{j} }[/math] means that out of each unit of output from sector i, how much percents it goes into sector j.

Based on these four matrices, we can produce some figures and setup a website to publish those figures on it so that readers can look up things like, for a given patent sector which scientific fields mainly compose its science fundation.

direct and indirect linkage

In the above analysis, we can only see the information coded in the direct citation matrix. Sometimes, an indirect linkage might be informative. For example, there might well be a case that sector [math]\displaystyle{ \mu }[/math] rarely directly cites field [math]\displaystyle{ i }[/math] but more often cite field [math]\displaystyle{ j }[/math], however due to the fact that field [math]\displaystyle{ j }[/math] heavily cites paper from field [math]\displaystyle{ i }[/math], effectively, the sector [math]\displaystyle{ \mu }[/math] relies heavily on support from field [math]\displaystyle{ i }[/math].

The general input-output analysis can integrate the direct and in-direct linkages among the scientific fields and patent sectors. Let us use the form of the original input-output analysis of Economics and once we understand that form, it is straightfoward to apply it here to the sci-tech linkage.

For an economy, we separate the industrial/agricultual/service sectors and the workers, and we call the latter the sector of final demands. We denote the former as the [math]\displaystyle{ N-1 }[/math] sector system and the final-demand sector as the sector [math]\displaystyle{ N }[/math]. We then have an input-output raw matrix [math]\displaystyle{ x^{i}_{j} }[/math] meaning the amount of value of the materails (or directly the materials) out of sector [math]\displaystyle{ i }[/math] that has been used by sector [math]\displaystyle{ j }[/math] in certain period of time that we are interested in.

Now, one may want to know that for each additional unit of product [math]\displaystyle{ j }[/math] consumed by the workers, or we say the sector [math]\displaystyle{ N }[/math], how the industrial/agricultual/service sectors should response. If we can know this information, then if somehow we can have an estimation of the consumption of products by the final demanders of the next time period, we can then obtain an estimation of the economic response to that expected change in the final demands.

So how we do that?

Leontief noticed that we have the following definition, [math]\displaystyle{ X^{i}=\sum_{j=1}^{N-1}x^{i}_{j}+x^{i}_{N} }[/math], which can be rewritten as [math]\displaystyle{ X^{i}=\sum_{j=1}^{N-1}\frac{x^{i}_{j}}{X^{j}}X^{j}+Y^{i} }[/math]. Using the difiition of matrix [math]\displaystyle{ B }[/math], we have [math]\displaystyle{ X^{i}=\sum_{j=1}^{N-1}B^{i}_{j}X^{j}+Y^{i} }[/math], which is a linear equation as follows, [math]\displaystyle{ X=BX+Y }[/math], Thus, [math]\displaystyle{ X=\left(1-B\right)^{-1}Y\triangleq L Y }[/math]. And since this is a linear relation, we can do a differentiation to get [math]\displaystyle{ \Delta X= L \Delta Y }[/math], which means that given an expected moification as [math]\displaystyle{ \Delta Y }[/math], what will be the response of the whole economic systemas [math]\displaystyle{ \Delta X }[/math].

We can also explain this in layman's term. In order to satisfy the final demander's dierct need [math]\displaystyle{ \Delta Y }[/math], the economic system first need to produce exactly [math]\displaystyle{ \Delta Y }[/math]. Then for the economic system to produce such [math]\displaystyle{ \Delta Y }[/math], it needs to prodduce the materials required to produce [math]\displaystyle{ \Delta Y }[/math] and that will be [math]\displaystyle{ B \Delta Y }[/math]. Again, for [math]\displaystyle{ B \Delta Y }[/math], we need [math]\displaystyle{ BB\Delta Y }[/math], and so on. Therefore, in total we need [math]\displaystyle{ \Delta X=\Delta Y+B\Delta Y+BB\Delta Y+\cdots }[/math]. This leads to exactly the same relation as the one wth the Leontief matrix [math]\displaystyle{ L }[/math].

What does this mean in terms of sci-tech linkage? It means that for a given demands from all the patents or a single patent sector on the scientific fields, how the science as a whole need to develop to satisfy the needs of the patents and more importantly, how such a required development will be distributed to various scientific felds.

Data and related issues

The original matrix [math]\displaystyle{ X }[/math] need to be extracted from publication and patent data. Jinshan's team has been working on APS papers and US patents, mainly the [math]\displaystyle{ S,ST }[/math] and [math]\displaystyle{ T }[/math] matrices. Wolfgang's team has been working on WOS publications and derwent patent data and they have covered data on all four matrices [math]\displaystyle{ S,ST,TS, T }[/math].

Another issue is which classification system to use and at what kind of granularity.

Furthermore, we may also need to decide to focus on the whole set of which scientific fields and patent sectors first, and what kind of time window should we choose to look at.

We should have discussion on those issue and then both Wolfgang's team and Jinshan's team will produce the raw matrix [math]\displaystyle{ X }[/math], which will be analyzed by Jinshan's team and both them will then discuss the implications of the results of analysis.

Plan

1. Discussion of the parameters for obtaining the matrix [math]\displaystyle{ X }[/math], time line and team members?
2. Producing the matrix [math]\displaystyle{ X }[/math], time line and team members?
3. Analyzing the matrix [math]\displaystyle{ X }[/math] to get both of the direct and indirect coefficients, time line and team members?
4. Discussion of the results and writing up papers if possible, time line and team members?

References

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